Mandelbrot: I See a Pattern

Benoit Mandelbrot (1924-2010), was a Polish-born, Jewish Mathematician, who migrated with his family to France in 1936 (where they acquired French citizenship). Poland had entered into a ‘Non-Aggression Pact’ with Nazi Germany in 1934 (which Hitler would annul in 1938 and break in 1939), but the Mandelbrot family, whilst escaping to the relative safety of France in 1936, had to eventually live under the Nazi German occupation of France which ran from 1940 – 1945. However, despite this danger, Benoit Mandelbrot (and his family) managed to live well, and assisted by the French Jewish community, he continued in is academic studies uninterrupted. After WWII, Mandelbrot held a number of academic positions, travelling to the US and Switzerland, before emigrating to the USA in 1958. He became embroiled as a young academic with the US computer development firm IBM. This association might be viewed as ironic today, considering the allegations that IBM, as an information and data collecting specialist, whilst operating out of New York during WWII, actively continued to collaborate and assist the Nazi German regime – apparently providing the reference system (and numbered tattoos) used by the Hitlerites to administer that terrible regime’s Concentration Camp and genocidal policy.

Complete Mandelbrot Set

However, despite the murky history and morally questionable associations, Benoit Mandelbrot was able, through the use of relatively primitive computers in 1980, to prove an idea held by a number of mathematicians throughout history (such as Georg Cantor whose pattern ‘set’ looked very much like the symbols used in the Chinese Classic of Change, and Helge von Koch – who worked from an equilateral triangle) – namely that mathematical equations form ‘real’ patterns in the physical world. Mandelbrot was able to perceive geometric patterns in his mind, when reading algebraic equations. He mathematically proved the existence of fractal patterns in the universe that continuously ‘branch’ off into similar, but different patterns which self-replicate forever in a continuously expanding manner (premised upon addition and multiplication). Although theoretical when expressed in numbers, the Mandelbrot Set is very similar to virtually all structures found within the natural world, and appears to be a scientific discovery of the pattern of existence itself. Of course, although some odd people have termed this the ‘thumb-print of god’, it is in fact a product of the steady development of science, mathematics and computer technology. Computer technology is required to express the immensity of the Mandelbrot Set, because it cannot be expressed by hand, due to its immense scope. These patterns continuously unfolding, covering more and more space, are magnified forever, and possess infinite precision. The patterns take on many different shapes and can be related to many living things. Essentially a Mandelbrot Set is a list of mathematical coordinates that when plotted on a graph, are forever expanding, self-modifying and self-replicating entities. The scientific assumption is that these patterns of numbers reflect the diversity of existence. This is a step further than the mandala found within Tibetan Buddhism (and favoured by Carl Jung), as the Mandelbrot Set does not, and cannot, ‘stop’ at any one ‘fixed’ geometric pattern, but instead routinely ‘grows’ out of, and beyond itself, with the movement of progression always being ‘forward’. These patterns look very similar to the non-structured images often perceived in the mind, and might be expressive of the ‘stuff’ from which thought arises. Whereas conventional religions always offer an answer in the distant future, the Mandelbrot Set offers a vision of reality here and now.